Price Jump Diffusion in Iranian Housing Market (Merton Model and NGARCH Approach)

Authors

Department of Economics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

This paper aims to model the housing price behavior in the Iranian market using three stochastic differential equations: the Black-Scholes model, Merton model, and geometric Brownian motion with nonlinear GARCH. The data of this study include monthly observations on housing prices between 2009 and 2018. Also, to estimate the coefficients of equations, we used the maximum likelihood approach, and the drift and diffusion parameters were calculated. The findings suggest that the efficient-market hypothesis does not hold in the Iranian housing market since the sudden jump under systematic risks is indicative of an increase in inefficiencies in the housing market. In this paper, we also use the nonlinear GARCH (NGARCH) model based on the Merton model to investigate the impact of good and bad news and positive and negative shocks. According to the results of the NGARCH model, housing price is more affected by bad news and negative shocks. According to the estimated equations in the Iranian housing market and the maximum likelihood function, the geometric Brownian model with stochastic NGARCH-based fluctuations has more explanatory power than the Merton model and the geometric Brownian model with constant volatility.

Keywords

References

Abolhasani, A., Ebrahimi, I., Pour Kazemi, M. H., & Bahraminia, E. (2016). The Effect of Oil Shocks and Monetary Shocks on Production and Inflation in The Housing Sector of The Iranian Economy: New Keynesian Dynamic Stochastic General Equilibrium Approach. Quarterly Journal of Economic Growth and Development Research, 7(25), 113–132.
Bardhan, A., Karapandža, R., & Urošević, B. (2006). Valuing Mortgage Insurance Contracts in Emerging Market Economies. The Journal of Real Estate Finance and Economics, 32, 9–20.
Brennan, M. J., & Schwartz, E. S. (1985). Evaluating Natural Resource Investments. The Journal of Business, 58(2), 135–157.
Calvo-Garrido, M. d C., & Vázquez, C. (2015). Effects of Jump-Diffusion Models for the House Price Dynamics in the Pricing of Fixed-Rate Mortgages, Insurance and Coinsurance. Applied Mathematics and Computation, 271, 730–742.
Chen, M. -C., Chang, C. -C., Lin, S. -K., & Shyu, S. -D. (2010). Estimation of Housing Price Jump Risks and Their Impact on the Valuation of Mortgage Insurance Contracts. Journal of Risk & Insurance, 77, 399–422.
Chen, Y. -T., Lai, W. -N., & Sun, E. W. (2019). Jump Detection and Noise Separation by a Singular Wavelet Method for Predictive Analytics of High-Frequency Data. Computational Economics, 54, 809–844.
Cho, M. (1996). House Price Dynamics: A Survey of Theoretical and Empirical Issues. Journal of Housing Research, 7(2), 145–172.
Dang, D. M., Nguyen, D., & Sewell, G. (2016). Numerical Schemes for Pricing Asian Options under State-Dependent Regime-Switching Jump–Diffusion Models. Computers & Mathematics with Applications, 71(1), 443–458.
Dewynne, J. N., Whalley, A. E., & Wilmott, P. (1994). Path-Dependent Options and Transaction Costs. Philosophical Transactions: Physical Sciences and Engineering, 347(1684), 517–529.
Englund, P., Gordon, T. M., & Quigley, J. (1999). The Valuation of Real Capital: A Random Walk down Kungsgatan. Journal of Housing Economics, 8(3), 205–216.
Ermogenous, A. (2006). Brownian Motion and Its Applications In The Stock Market. Ecommons, Retrieved from https://ecommons.udayton.edu/cgi/viewcontent.cgi?article=1010&context=mth_epumd
Fan, G. -Z., Pu, M., Deng, X., & Ong, S. E. (2018). Optimal Portfolio Choices and the Determination of Housing Rents under Housing Market Uncertainty. Journal of Housing Economics, 41, 200–217.
Fuh, C. -D., Teng, H. -W., & Wang, R. -H. (2018). Efficient Simulation of Value-at-Risk Under a Jump Diffusion Model: A New Method for Moderate Deviation Events. Computational Economics, 51, 973–990.
Gholizade, A. A., & Bakhtiari Pour, S. (2012). The Impact of Credit on Housing Price in Iran. Iranian Journal of Applied Economic Studies, 1(3), 159–179.
Gholizade, A., & Noroozonejad, M. (2019). Dynamics of Housing Prices and Economic Fluctuations in Iran with the Approach of Dynamic Stochastic General Equilibrium (DSGE). JSE, 9(36), 37-74.
Gibson, R., & Schwartz, E. S. (1990). Stochastic Convenience Yield and the Pricing of Oil Contingent Claims, 45(3), 959-976.
Gu, H., Liang, J. -R., & Zhang, Y. -X. (2012). Time-changed Geometric Fractional Brownian Motion and Option Pricing with Transaction Costs. Physica A: Statistical Mechanics and Its Applications, 391(15), 3971–3977.
Heston, S. L. (1993). A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies, 6(2), 327–343.
Hwang, M., & Quigley, J. M. (2010). Housing Price Dynamics in Time and Space: Predictability, Liquidity, and Investor Returns. The Journal of Real Estate Finance and Economics, 41, 3–23.
Kou, S. G. (2002). A Jump-Diffusion Model for Option Pricing. Management Science, 48(8), 1086–1101.
Li, Z., Zhang, W. -G., Liu, Y. -J., & Zhang, Y. (2019). Pricing Discrete Barrier Options under Jump-Diffusion Model with Liquidity Risk. International Review of Economics & Finance, 59(C), 347–368.
Meen, G. (2002). The Time-Series Behavior of House Prices: A Transatlantic Divide? Journal of Housing Economics, 11(1), 1–23.
Merton, R. C. (1976). Option Pricing when Underlying Stock Returns are Discontinuous. Journal of Financial Economics, 3(1–2), 125–144.
Merton, R. C. (1973). An Intertemporal Capital Asset Pricing Model. Econometrica, 41(5), 867–887.
Mousavi, M., & Doroodian, H. (2016). Analyzing the Determinants of Housing Prices in Tehran City. Economic Modeling, 9(31), 103–127.
Nademi, Y., & Khochiany, R. (2017). Considering the Relationship between the Housing Sector and Some Macroeconomic Variables of Iran: The Wavelet Coherency Approach. Journal of Econometric Modelling, 2(4), 85–106.
Rambeerich, N., & Pantelous, A. A. (2016). A High Order Finite Element Scheme for Pricing Options under Regime Switching Jump Diffusion Processes. Journal of Computational and Applied Mathematics, 300, 83–96.
Rambeerich, N., Tangman, D. Y., Gopaul, A., & Bhuruth, M. (2009). Exponential Time Integration for Fast Finite Element Solutions of Some Financial Engineering Problems. Journal of Computational and Applied Mathematics, 224(2), 668–678.
Rambeerich, N., Tangman, D. Y., Lollchund, M. R., & Bhuruth, M. (2013). High-order Computational Methods for Option Valuation under Multifactor Models. European Journal of Operational Research, 224(1), 219–226.
Scholes, M., & Black, F. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637–654.
Schwartz, E. S. (1997). The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging. The Journal of Finance, 52(3), 923–973.
Tian, Y., & Zhang, H. (2020). European Option Pricing under Stochastic Volatility Jump-Diffusion Models with Transaction Cost. Computers & Mathematics with Applications, 79(19), 2722–2741.
Iranian Economic Review
Volume 26, Issue 2
June 2022
Pages 369-388

Files

Share

How to cite

Statistics